Among Kaplan's most influential contributions to the philosophy of language is his semantic analysis of indexicals and demonstratives, which is outlined (in progressively greater detail) in "Dthat," "On The Logic of Demonstratives," "Demonstratives," and "Afterthoughts".

Kaplan's insights center around two key distinctions, which may be seen as made in response to the inability of Frege's semantics to deal with context-sensitivity in language. First, in place of Frege's category of Sinn (Sense: roughly meaning or content), Kaplan introduces the notions of character and content, where the former can be thought of roughly as the meaning of an expression, and the latter can be thought of as the proposition (or propositional component) expressed by an expression in a context. Along with this distinction, Kaplan makes the explicit distinction between the context of an utterance and the circumstances of evaluation of the proposition expressed by an utterance. Context can be formalized as a set composed of a speaker, a place, a time, and a possible world (and, depending on the analysis of demonstratives, perhaps a set of either demonstrations or directing intentions). Circumstances of evaluation play a role very similar to possible worlds in modal semantics.

With all these notions in place, Kaplan gives a more technical definition of character and content. Character defines a function associated by convention with an expression, which takes contextual elements as arguments and yields content as values. Content, on the other hand, defines a function taking as arguments those elements of the circumstances of evaluation relevant to determining extension, and outputting as a value the extension (referent or truth value).

Two more important notions can thus be defined. We can say that an expression is context-sensitive just in case its character defines a non-constant function (i.e. just in case it outputs different content-values given different context-element-arguments). An expression is context-insensitive just in case its character defines a constant function. We might also say that the distinction between character and content breaks down in the case of context-insensitive exspressions, and that convention associates each such expression directly with a content.

On the other hand, an expression is directly referential just in case its content defines a constant function from circumstances of evaluation to extension. Kaplan also characterizes directly referential expressions as those which refer without the mediation of a Fregean Sinn, or as those whose only contribution to content are their referents. Thus, in the case of directly referential expressions, we can say that the distinction between content and referent breaks down.

Context-sensitive expressions, it turns out, are basically all directly referential according to Kaplan and others (e.g. see John Perry, "Frege on Demonstratives" in The Problem of the Essential Indexical and Other Essays). So the following intuitive picture emerges: the meaning of an indexical is a rule taking us from some part of the context to an extension, and the meaning of a non-indexical is a bit of propositional content which determines the extension in each possible world.

Kaplan goes on to use this semantic scheme to explain interesting phenomena concerning things like the relationship between necessary and a priori truth. An utterance is said to be necessarily true just in case the content it expresses is true in every possible circumstance; while an utterance is said to be true a priori just in case it expresses, in each context, a content which is true in the circumstances of which that context is a part. So, 'I am here now' is true a priori in virtue of the fact that each of the indexical expressions used ('I', 'here', 'now') directly refer to the speaker, location, and tme of utterance. But the utterance is not necessarily true, because any given speaker might have been in at a different place at that time given different circumstances of evaluation. On the other hand, 'I am David Kaplan,' as spoken by David Kaplan, is necessarily true, since 'I' and 'David Kaplan' (both directly referential expressions) refer to the same object in every circumstance of evaluation. The same statement is not true a priori, however, because if it were spoken in a different context (i.e. one with a speaker other than Kaplan), it might be false.

Another nice result of Kaplan's theory is that it solves Frege's Puzzle for indexicals. Roughly, the puzzle in this incarnation results from the fact that indexicals are thought to be directly referential, which is also to say that they do not refer by means of a Fregean Sinn. But Frege explained the cognitive value in terms of Sinn. Thus the following problem emerges: The sentences "I am David Kaplan," spoken by David Kaplan, "He is David Kaplan," spoken by someone pointing at David Kaplan, and "David Kaplan is David Kaplan," spoken by anyone, all express the same content and refer to the same individuals. Yet each of the three has a different cognitive value (it is possible to rationally believe one while denying another). Kaplan explains this by associating cognitive value with character rather than content, thus remedying the problem. (There are problems with this approach, which Kaplan explores in "Afterthoughts".

Perhaps the central problem faced by Kaplan's approach is that of proper names. The problem stems from the fact that proper names seem to be both directly referential and context-insensitive, which means that constant functions are defined by both a proper name's character and its content. This seems to suggest, however, that proper names have no meaning other than their reference--a view originally proposed by John Stuart Mill, but thrown into doubt by Frege with the version of his puzzle for proper names. Many philosophers have attempted to deal with this issue (notably Scott Soames, Nathan Salmon, Howard Wettstein, Michael Devitt, David Braun, and Joseph Almog), but without resounding success.

"On the Logic of Demonstratives," Journal of Philosophical Logic, VIII 1978: 81-98; and reprinted in French et. al. (eds.), Contemporary Perspectives in the Philosophy of Language (Minneapolis: University of Minnesota Press, 1979): 401-412.